Schlesser was born in the French colony of Madagascar in 1928. It was only after the war that he moved to France and studied in Nancy before getting a job in a factory which manufactured adding machines. He began racing only when he was 24, driving a Dyna-Panhard in the Rally of Lorraine. He was then posted back to Madagascar and his career in the sport stopped until he returned and bought himself a Triumph TR2. He promptly destroyed it and several other cars and so went back to Madagascar, flying to France to race only during his holidays. After surviving an accident when he drove a Ferrari into a ravine, he decided to become a professional racing driver and bought a Cooper Formula 3 car from Harry Schell. He was quick but had a lot of accidents.

He was seriously injured in a crash in practice for the Le Mans 24 Hours in 1961 but he refused to give up and went into business with Ligier in a Ford dealership in Paris, a connection which helped him land a job with the Ford France team in 1963. In 1964 he went to the United States and raced stock cars, an unusual move at the time.

In 1966 he raced a Formula 2 Matra in the German Grand Prix and he did the same the following year but his desire to be a Grand Prix driver, despite being 40, led him to accept an invitation to drive the untested air-cooled Honda RA302 in the 1968 French Grand Prix at Rouen. Built of magnesium - to reduce weight - the car was tested by John Surtees who felt that it was not ready to race but Honda wanted to push ahead and so the car was given to Schlesser. In the famous fast sweepers going downhill at Rouen Schlesser lost control of the car. It hit a bank, overturned and caught fire. Schlesser was killed. Ligier later designated all his cars "JS" after his friend Schlesser.